Prerequisite Basic Calculation Skills for Calculus Algebra: A Content Analysis of Student Responses

Calculus and Algebra is a foundational mathematics course in Malaysian polytechnics that requires students to possess stable prerequisite basic calculation skills to engage effectively with higher-level mathematical concepts. Despite prior exposure to mathematics at the secondary school level and in earlier semesters, many students particularly those from diverse educational backgrounds, continue to experience difficulties in mastering the course. This study aims to explore students’ prerequisite basic calculation skills for the Calculus and Algebra course using a qualitative approach. A diagnostic test consisting of ten short-answer questions was administered at the beginning of the semester to assess fundamental arithmetic and elementary algebra skills, including numerical operations, algebraic manipulation, equation solving, and symbolic interpretation. The data were analysed using deductive qualitative content analysis, guided by a coding framework adapted from the Calculus and Algebra course syllabus and commonly recognized prerequisite mathematical competencies. Students’ written responses were examined across four content domains. The findings indicate that students’ prerequisite basic calculation skills are largely unstable and inconsistently applied. While some students demonstrated surface-level familiarity with basic procedures, many exhibited partial understanding, conceptual misunderstandings, or an inability to initiate appropriate solution strategies. Blank responses further suggested limited conceptual readiness and confidence. Overall, students’ prior knowledge was fragmented, with a strong reliance on memorized procedures rather than conceptual understanding. This research highlights substantial gaps in prerequisite basic calculation competencies as well as underscores importance of early diagnostic assessment and targeted foundational reinforcement to improve students’ readiness for learning Calculus and Algebra in the polytechnic context.